

A016957


a(n) = 6*n + 4.


42



4, 10, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82, 88, 94, 100, 106, 112, 118, 124, 130, 136, 142, 148, 154, 160, 166, 172, 178, 184, 190, 196, 202, 208, 214, 220, 226, 232, 238, 244, 250, 256, 262, 268, 274, 280, 286, 292, 298, 304, 310, 316, 322, 328
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OFFSET

0,1


COMMENTS

Number of 2 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01,1) and (11;0). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1<i2, j1<j2 and these elements are in the same relative order as those in the triple (x,y,z). In general, the number of m X n 01 matrices in question is given by (n+2)*2^(m1)+2*m*(n1)2 for m>1 and n>1.  Sergey Kitaev, Nov 12 2004
If Y is a 4subset of an nset X then, for n>=4, a(n4) is the number of 3subsets of X having at least two elements in common with Y.  Milan Janjic, Dec 08 2007
4th transversal numbers (or 4transversal numbers): Numbers of the 4th column of positive numbers in the square array of nonnegative and polygonal numbers A139600. Also, numbers of the 4th column in the square array A057145.  Omar E. Pol, May 02 2008
a(n) is the maximum number such that there exists an edge coloring of the complete graph with a(n) vertices using n colors and every subgraph whose edges are of the same color (subgraph induced by edge color) is planar.  Srikanth K S, Dec 18 2010
Also numbers having two antecedents in the Collatz problem: 12*n+8 and 2*n+1 (respectively A017617(n) and A005408(n)).  Michel Lagneau, Dec 28 2012


REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 189.  From N. J. A. Sloane, Dec 01 2012


LINKS

Table of n, a(n) for n=0..54.
Tanya Khovanova, Recursive Sequences
S. Kitaev, On multiavoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
Index to sequences related to polygonal numbers
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

A008615(a(n)) = n+1.  Reinhard Zumkeller, Feb 27 2008
a(n) = A016789(n)*2.  Omar E. Pol, May 02 2008
A157176(a(n)) = A067412(n+1).  Reinhard Zumkeller, Feb 24 2009
a(n) = sqrt(A016958(n)).  Zerinvary Lajos, Jun 30 2009
a(n) = 2*(6*n+1)a(n1) (with a(0)=4).  Vincenzo Librandi, Nov 20 2010
a(n) = floor((sqrt(36*n^236*n+1)+6*n+1)/2).  Srikanth K S, Dec 18 2010
From Colin Barker, Jan 30 2012: (Start)
G.f.: 2*(2+x)/(12*x+x^2).
a(n) = 2*a(n1)a(n2). (End)
A089911(2*a(n)) = 9.  Reinhard Zumkeller, Jul 05 2013
a(n) = 3 * A005408(n) + 1.  Fred Daniel Kline, Oct 24 2015
a(n) = A057145(n+2,4).  R. J. Mathar, Jul 28 2016
a(4*n+2) = 4 * a(n).  Zhandos Mambetaliyev, Sep 22 2018


MAPLE

seq(6*n+4, n = 0 .. 50) # Matt C. Anderson, Jun 09 2017


MATHEMATICA

Range[4, 1000, 6] (* Vladimir Joseph Stephan Orlovsky, May 27 2011 *)


PROG

(Maxima) makelist(6*n+4, n, 0, 30); /* Martin Ettl, Nov 12 2012 */
(Haskell)
a016957 = (+ 4) . (* 6)  Reinhard Zumkeller, Jul 05 2013
(PARI) a(n)=6*n+4 \\ Charles R Greathouse IV, Jul 10 2016


CROSSREFS

Cf. A008588, A016921, A016933, A016945, A016969, A000217, A017329, A057145, A139600, A139606, A016958.
Sequence in context: A189932 A310533 A269960 * A109273 A294636 A295560
Adjacent sequences: A016954 A016955 A016956 * A016958 A016959 A016960


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



